Cold and calculating careerists will no doubt be confused by Jillette Johnson’s determination to fix something that isn’t broken. The New York–based singer-songwriter has received plenty of positive attention for her debut full-length, Water in a Whale, with critics comparing her favourably to the likes of sad-girl antiheroine Fiona Apple and art-star Regina Spektor.

If the album proves anything, it’s that Johnson certainly knows how to play the piano, an instrument she began mastering in elementary school. Songs rely heavy on the ivories, often augmented by string arrangements that are both bold and tasteful.

Water in a Whale has put Johnson on the international pop radar, with profiles on the web everywhere from Last.FM to Slacker, and opening slots for artists including Macklemore collaborator Mary Lambert. Her response to the recognition so far? That would be to rip up her one playbook and start all over, as she has on her current tour.

“I’m actually not playing piano so much any more,” Johnson says, on the line from a tour stop “somewhere in Illinois”. “I’ve got a ’70s Wurlitzer, and I’ve now committed to only playing that during shows. It’s been really nice. As much as I love the piano, and grew up playing the piano, I find that piano can be a sort of sweeter-sounding instrument that takes up a lot of space. I have a really big voice, and I’m also incredibly lyrically driven, so I’m trying to find a way to let that come through in my songs a little bit more.”

Those lyrically driven songs are often unflinching, with the 24-year-old chanteuse chronicling everything from lost party weekends (“Peter Pan”) to making one’s way in a world that’s moving too fast for most of us to hang on to (“Last Bus Out”). At times Johnson can be devastating in her observations. The spartan piano number “Pauvre Coeur”, for example, lays out a crumbling relationship with lyrics like “You were high and watching poker, and I had just walked in the door/You started screaming at the TV, saying, make a play you filthy whore,” followed by the final line: “I am far too beautiful to be yours.”

The track that’s really got all the attention is “Cameron”, a powerful ballad about entering the world as a boy, but knowing from the start you are really a girl, a song that resonates with anyone who has ever felt like an outsider.

Given the often heavy subject matter on Water in a Whale, one might wonder if Johnson used the album to work some things out. The singer allows that there’s some truth to that, but stops short of declaring herself to be someone prone to wallowing in a bottomless pit of despair.

“When I was writing the record,” Johnson says, “I think that I was in the place that I’m always in, which is pretty in tune with what’s going on around me, and kind of along for the ride and the experiences and really going through the whole emotional journey. But also not letting anything destroy my life. That’s one of the wonderful things about songwriting. You can experience things and work to get it out there so it doesn’t poison you. You’re letting it out instead of keeping it in.”

From the reaction to Water in a Whale, it’s obvious that Johnson is connecting with plenty of folks out there, most of whom would probably love her to keep doing what she’s been doing.

That isn’t going to happen, however.

“I’m in a place with writing now that feels really different and awesome,” Johnson says. “And I really like sonically where I’m going. But I want to make sure this next album is pretty amazing, so right now I’m mostly being pretty hard on myself.”

Jillette Johnson opens for Mary Lambert at the Rio on Saturday (November 15).